Theoretical stellar luminosity functions and the ages and compositions of globular clusters

Ratcliff, S. J.

doi:10.1086/165361

Cited by 13 publications

(7 citation statements)

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“…The LF seems to be the most natural observable to try to constrain both age (15,16) and distance modulus at the same time. The LF is a natural clock because the number of stars in a given luminosity bin decreases with time, because more massive stars evolve more rapidly than less massive ones.…”

Section: The Luminosity Function Methodsmentioning

confidence: 99%

Globular cluster ages

Jiménez

1998

Proc. Natl. Acad. Sci. U.S.A.

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We review two new methods to determine the age of globular clusters (GCs). These two methods are more accurate than the classical isochrone fitting technique. The first method is based on the morphology of the horizontal branch and is independent of the distance modulus of the globular cluster. The second method uses a careful binning of the stellar luminosity function and determines simultaneously the distance and age of the GC. We find that the oldest galactic GCs have an age of 13.5 ؎ 2 gigayears (Gyr). The absolute minimum age for the oldest GCs is 10.5 Gyr (with 99% confidence) and the maximum 16.0 Gyr (with 99% confidence). Therefore, an Einstein-De Sitter Universe (⍀ ‫؍‬ 1) is not totally ruled out if the Hubble constant is about 65 ؎ 10Galactic globular clusters (GCs) are the best stellar clocks to establish a lower limit to the age of the universe. Nevertheless, a robust age for the oldest GCs is yet to be determined. GCs are excellent stellar clocks because they fulfill the following properties:• All the stars were born at the same time.• The population is chemically homogeneous.• There has not been any further episodes of star formation that gave birth to new stars, which could cover up the oldest population.Support for GCs being old comes from two facts: their metallicity is as low as 1͞100 of solar and the characteristics of their color magnitude diagram (CMD) are those corresponding to ages larger than 10 gigayears (Gyr), i.e., the stars around the main sequence turn-off (MSTO) have masses lower than 1 M J .Despite the continuous effort carried out during more than 30 years to give a precise value for the age of GCs, the uncertainty in their age still remains at about 4 Gyr. The problem is particularly complicated because age and distance have the same effect on the morphology of the MSTO point. Deficiencies in the input physics combined with the uncertainties in cluster distances and interstellar reddening have made it difficult to determine GC ages with an accuracy better than about 25%.In this review I present two alternative methods used to derive ages of GCs that are independent of the traditional MSTO fitting. The first method is based on the morphology of the horizontal branch (HB) and uses the reddest points in the HB to determine the mass of the stars in the red giant branch (RGB) (1). This method is independent of the distance modulus and therefore is a useful tool to compute systematics in ages determinations by using the traditional MSTO fitting technique. The second of the methods is based on a careful binning of the luminosity function (LF) and determines simultaneously the age and distance of a GC. It therefore is a very useful technique to determine distances to GC independently of the subdwarf fitting and RR-Lyrae techniques. It is also very powerful to determine relative ages of GCs with little error.In the next sections I describe the traditional isochrone fitting method and the HB morphology and LF methods. I finish with a discussion on the uncertainties of the different...

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Section: The Luminosity Function Methodsmentioning

confidence: 99%

Globular cluster ages

Jiménez

1998

Proc. Natl. Acad. Sci. U.S.A.

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“…The subgiant branch is also the portion of the LF most affected by the specifics of the chemical composition. The helium abundance exerts a great effect on the SGB (Simoda 1972), while leaving the relative numbers of stars on the RGB and MS mostly unchanged (Ratcliff 1987). A decrease in helium abundance causes the slope of the SGB in the CMD to become shallower.…”

Section: The Subgiant Branchmentioning

confidence: 99%

“…Taken together with the evidence for metal-poor clusters like M92 and M30, this may be an indication of a metal-dependent trend. A few input parameters can change the relative levels (Ratcliff 1987). The initial mass function (IMF) exponent that is used in the theoretical LF can change the normalization of the MS, but it also changes the shape of the MS portion of the LF.…”

Section: The Ms-rgb Discrepancymentioning

confidence: 99%

CCD Photometry of the Globular Cluster M5. I. The Color-Magnitude Diagram and Luminosity Functions

Sandquist¹,

Bolte²,

Stetson³

et al. 1996

ApJ

125

199

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We present new BV I photometry for the halo globular cluster M5 (NGC 5904 = C1516+022), and examine the B-and I-band luminosity functions (LFs), based on over 20,000 stars -one of the largest samples ever gathered for a cluster luminosity function. Extensive artificial star tests have been conducted to quantify incompleteness as a function of magnitude and cluster radius. We do not see evidence in the LF of a "subgiant excess" or of a discrepancy in the relative numbers of stars on the red-giant branch and main sequence, both of which have been claimed in more metal-poor clusters.Enhancements of α-element have been taken into account in our analysis. This improves the agreement between the observed and predicted positions of the "red-giant bump". Depending on the average α-element enhancement among globular clusters and the distance calibration, the observed discrepancy between the theoretical and observed position for a large number of clusters ) can be almost completely removed.The helium abundance of M5, as determined by the population ratio R, is found to be Y = 0.19 ± 0.02. However, there is no other indication that the helium abundance is different from other clusters of similar metallicity, and values calculated for other helium indicators are consistent with Y ≈ 0.23.The relative ages of M5, Palomar 5, M4, NGC 288, NGC 362, NGC 1261, NGC 1851 and NGC 2808 are derived via the ∆V HB T O method using M5's horizontal branch (HB) as a bridge to compare clusters with very different HB morphology. We conclude that at the level of ∼ 1.5 Gyr these clusters of comparable metallicity are the same age with the possible exception of NGC 288 (older by 3.5 ± 1.5 if the reddest NGC 288 HB stars are on the zero-age horizontal branch) and Palomar 5 (which may be marginally younger). Even with NGC 288 set aside, there is a large range in HB morphology between the remaining clusters which appears to eliminate age as the sole second parameter determining HB morphology in the case of constant mass loss between RGB and HB (although a Reimers' mass-loss relation weakens this statement considerably).We are unable to chose between the two competing values for M5's (absolute) metallicity: [Fe/H] = −1.40 (Zinn & West 1984) and −1.17 (Sneden et al. 1992) based on recent high-dispersion spectroscopy. This level of discrepancy has a signifcant effect on the derivation of the distance modulus and absolute age of M5. From subdwarf fitting to the main sequence of the cluster, we find an apparent distance modulus (m − M ) V = 14.41 ± 0.07 for [Fe/H] M5 = −1.40, and 14.50 ± 0.07 if [Fe/H] M5 = −1.17. From comparisons with theoretical isochrones and luminosity functions, we find an absolute age for M5 of 13.5 ± 1 Gyr (internal error, assuming perfect models and no [M /H] error) for the Zinn & West abundance scale and 11 ± 1 Gyr for the higher abundance value.

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“…The abundance of helium and CNO elements enter into the determination of the instantaneous nuclear reaction rate at any point in a star, yet theoretical models indicate that the abundance of CNO elements does not significantly affect the relative numbers of RGB and MS stars while helium abundance plays a more substantial role (Stetson 1991;VandenBerg, Larson, & de Propris 1998). The reason for this can be seen in the study of Ratcliff (1987) -the evolutionary timescale for red giants is not changed by variations in helium abundance, but the MS timescale is. We believe that this can be understood qualitatively as being due to the nature of the structure of red giants: the rate of nuclear reactions in the hydrogen fusion shell is set entirely by the star's need to support the envelope and the position of the shell source (set by the size of the degenerate core).…”

Section: Discussionmentioning

confidence: 99%

The Unusual Luminosity Function of the Globular Cluster M10

Pollard

Sandquist

Hargis

et al. 2005

ApJ

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We present the I-band luminosity function of the differentially reddened globular cluster M10. We combine photometric analysis derived from wide-field (23' x 23') images that include the outer regions of the cluster and high-resolution images of the cluster core. After making corrections for incompleteness and field star contamination, we find that the relative numbers of stars on the lower giant branch and near the main-sequence turnoff are in good agreement with theoretical predictions. However, we detect significant (> 6 \sigma) excesses of red giant branch stars above and below the red giant branch bump using a new statistic (a population ratio) for testing relative evolutionary timescales of main-sequence and red giant stars. The statistic is insensitive to assumed cluster chemical composition, age, and main-sequence mass function. The excess number of red giants cannot be explained by reasonable systematic errors in our assumed cluster chemical composition, age, or main-sequence mass function. Moreover, M10 shows excesses when compared to the cluster M12, which has nearly identical metallicity, age, and color-magnitude diagram morphology. We discuss possible reasons for this anomaly, finding that the most likely cause is a mass function slope that shows significant variations as a function of mass.Comment: 31 pages, 12 figures, accepted for Ap

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Theoretical stellar luminosity functions and the ages and compositions of globular clusters

Cited by 13 publications

References 0 publications

Globular cluster ages

Globular cluster ages

CCD Photometry of the Globular Cluster M5. I. The Color-Magnitude Diagram and Luminosity Functions

The Unusual Luminosity Function of the Globular Cluster M10

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